 # Systems of Equations Word Problem #7

okay so for this problem Victoria we're going to again use substitution to solve it so I'm go from the table and set up the systems of equations so this equation will be d equals so speed 53 times time and then the second equation will be the expression for 40 minus D equals 49 times time let's clear that up look at 49 times time so I'm gonna use substitution again I'm taking this expression and replacing D with that expression so my new equation is 440 minus D but D from the previous equation is the 53 T and it equals 49 T okay so at this point you would add 253 t to the other side so that gives you 4 for T equals what is that 90-100 2t and what would you do at this step so correct divided by 102 so then I have time and my time equals four point I have to round this one so let's say four points three hours now I have a decimal answer so sometimes like students if I have a decimal answer actually if I have a decimal answer that's not a decimal it terminates like four point five or four point two then I'll go back and double check because the the directions didn't indicate that we should round which will make me think it would not terminate correct if she would terminate but it didn't someone go back to double check and then see if burying mistakes so we have distance okay so then let's go and let me double check by I looked at the reread the problem and convinced myself that the setup was accurate so then I mean let's try to see what the distances are so for distance of the distance for training one equals fifty three times T but the time is about forty three correction 4.3 hours so let's use a calculator so 4.3 times 53 that gives me about two hundred twenty seven point nine miles okay now let's calculate the distance for the second training so that's distance equals speed times time so 49 times four point three so 49 times four point three and then that gives me two ten point seven miles okay knowing at this number and this number so that's two twenty seven point nine okay and the answer I have is about four thirty eight point six miles now that's not 440 miles so why do you think the answer that we got is not exactly the same as 440 miles why is this number here not exactly the same as the 440 miles and we just said this is because of the time remember our time was a number that we round it so whenever you round in the case of a word problem it affects the accuracy just a little bit so for thirty eight point six is close enough to four forty to convince me that the setup is correct okay let me know if it let me know if you have questions on this problem during our session